Are rebadged & rebranded synonyms, or do they have different meanings?

Besides cosmetic changes, drive model identifiers & firmware, how can rebadged and/or rebranded drives differ from the original drive specs? e.g., can any of the following either be added or subtracted by a rebadge / rebrand: AccurateStream, C2 detection, HTOA support, audio caching, lead in or out overread, disc format support, etc.?